Flight & Safety Design

Wing Design for

the ECO1 Aircraft Using the CFD Tool Ansys Fluent

Gregor McKechnie

2016-06-29

Masters Thesis at Aeronautical and Vehicle Engineering

Supervisor: Prof. Revstedt (LTH)

Examiner: Prof. Rizzi (KTH)

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Abstract An analysis of a new wing for the ECO1 general aviation aircraft. A new wing for this aircraft is hoped to provide better high-lift performance and a higher maximum angle of attack. To this end, using computational fluid dynamics with the SST k-ω turbulence model, this study explores modifying the wing profile and augmenting the wings with winglets, a feature not commonly used in general aviation. Using the CFD tool Fluent, two-dimensional simulations on variations of the Osquavia aerofoil indicate that both the slimmer and the elongated variants will provide for a greater maximum coefficient of lift and a higher stall angle. The three-dimensional CFD analysis predict that the winglets will decrease the overall drag in high lift-coefficient flight conditions without greatly penalising performance in the cruise condition. The addition of winglets are also shown to provide a higher angle of stall and improve flow across the control surfaces at high angles of attack.

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Contents Nomenclature ........................................................................................................... 3

1 Background & Aim ........................................................................................... 4

2 Using Computational Fluid Dynamics............................................................... 5

2.1 Domain Size ............................................................................................... 5

2.2 Structured vs. Unstructured Mesh ............................................................... 5

2.3 Mesh Refinement ........................................................................................ 7

2.4 Mesh Growth Rate ...................................................................................... 8

2.5 Boundary Conditions .................................................................................. 8

2.6 Solution Settings ......................................................................................... 8

2.6.1 Coupling ............................................................................................ 8

2.6.2 Spatial discretization .......................................................................... 8

2.6.3 Solution Controls ............................................................................... 9

2.7 Viscous Models .......................................................................................... 9

2.7.1 Spalart-Allmaras Model ..................................................................... 9

2.7.2 The k-ω with SST Model ................................................................... 9

2.7.3 The k-kl-ω Model .............................................................................. 9

2.8 Results ...................................................................................................... 10

3 Study 1: The Aerofoil ..................................................................................... 13

3.1 Modifying the Stall Characteristics ........................................................... 13

3.2 Conclusion ................................................................................................ 13

4 Study 2: Winglets ........................................................................................... 14

4.1 Background & Theory .............................................................................. 14

4.2 Three-Dimensional Mesh Methods ........................................................... 14

4.2.1 Mesh Structure................................................................................. 14

4.2.2 Domain Size .................................................................................... 14

4.3 Results ...................................................................................................... 15

4.3.1 Comparison of a half-wing with and without a winglet .................... 15

4.3.2 Optimisation of toe-out angle of winglet segment with the help of the mesh-morphing tool ........................................................................................ 18

4.3.3 An analysis of the effect on CD ........................................................ 21

4.3.4 Visualisation of Winglet Effect on Wing-Tip Vortices ..................... 22

4.3.5 Visualisation of the Stall Development ............................................ 23

4.3.6 Discussion of the Visualisation of the Stall Development ................. 28

5 Conclusions .................................................................................................... 29

6 Further study................................................................................................... 30

7 References ...................................................................................................... 31

8 Acknowledgements ......................................................................................... 31

Appendix - Some Further Notes on the Use of Fluent ............................................. 32

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Nomenclature α angle of attack of wing with respect to direction of travel CD coefficient of drag CL coefficient of lift CL_α lift curve slope CM coefficient of moment ε turbulent dissipation, the scale of the turbulence

k turbulent kinetic energy LES Large Eddy Simulation LSA Light Sports Aircraft ω specific dissipation SST shear stress transport ϑ the angle of toe-out of the winglet with respect to the x axis

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1 Background & Aim The private aviation market, with its focus on safety, is naturally a conservative market. The world's fleet of aircraft consists of large numbers of elderly aircraft, not only in terms of flying hours but particularly in terms of design. In the near future the industry must expect tougher environmental standards to be placed upon it. This means that increased aerodynamic efficiency and engine efficiency will become of paramount importance. Manufacturers are already responding with leaner engines and slipperier airframes. Relatively new to Europe is the class of aircraft Light Sports Aircraft. This classification has already existed in Australia and the USA for some time and now the first such aircraft have been certified in Europe. The class is chiefly characterised by the maximum take-off weight being limited to 600 kg[1.1][1.2][1.3]. The ECO1 aircraft design is derived from the Osqavia project initiated at the Royal Institute of Technology in Stockholm (KTH) between the years 1986 and 1994. The prototype project was later taken on by Niklas Anderberg who, with assistance from the industrial school at SAAB, completed the construction of prototype aircraft to fly it under an experimental classification. The aircraft provides exceptional high speed for its class combined with good fuel efficiency. Flight tests have shown it have an asymmetrical, gentle and predictable stall and also to be capable of recovering from a spin. Having founded the company Flight & Safety Design the goal is to further develop the design of Osqavia and market it as a Light Sports Aircraft. The new evolution of the design strives for even higher aerodynamic efficiency and engine efficiency. The engine on offer will either be the HKS 700T or the new Rotax 600. In order to decrease the form drag, the taper of the fuselage has been made more gradual. This study will investigate two possible modifications to further improve upon the design of the Osqavia:

• Variations of the aerofoil profile in order to change the wing loading and improve stall characteristics

• The addition of winglets to the main wing in order to decrease induced drag in high lift flight conditions and improve stall characteristics.

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2 Using Computational Fluid Dynamics This study has aimed to compare the relative benefits of different wing designs by using the computational fluid dynamics (CFD) tool Fluent. A multitude of settings are available. Some experimentation was carried out with various turbulence models, solution methods and solution controls. For the two-dimensional work, meshes were created using both ICEM-CFD and Ansys Meshing. Some experimentation was carried out with different shapes of the mesh zone, mesh types and mesh fineness. What follows is a short description of some of the basic settings in Fluent used throughout the work, which are considered suitable for simulations of external aerodynamics.

2.1 Domain Size

Literature on the subject recommends that the test domain area or volume should extend 25 times the significant length of the test subject along the direction of the wake. In the two-dimensional simulations the computing power available was such that this was not a limiting factor. However, in the three-dimensional simulations, the computer memory initially available did put certain limitations to the number of cells in the actual mesh construction phase and its import into Fluent.

2.2 Structured vs. Unstructured Mesh

Two different approaches were experimented with when running two-dimensional simulations. One of those was to use a structured mesh, produced using the tool ICEM CFD. Rather than rotating the aerofoil with respect to the test domain and the air stream it was expedient to keep the whole test domain, with the aerofoil and the mesh within it, fixed and instead rotate the angle of incidence of the free air stream. This was done by means of adjusting the vectors of the free stream in the boundary conditions settings of Fluent. In order to avoid any complications at non-zero angles of attack, such as reverse flow across upper or lower surfaces a rectangular box test domain was not used. Instead a parabolic area, see Figure 1, was used with an acuteness such that, within the range of angles of attack simulated, the flow would always flow in the positive direction across the surface defined as the inlet. The structured mesh used here is computationally efficient, both in production of the mesh and during the CFD computation. It does, however, require more manual labour in setting up, becoming more difficult the more complex the geometry being tested.

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Figure 1 The parabolically shaped structured domain about a NACA 23012 aerofoil profile.

Figure 2 A close up the trailing edge of the NACA 23012 aerofoil profile showing the structured nature of the mesh.

The alternative is to use an unstructured mesh. The unstructured mesh lends itself to using the mesh automation features available in the ANSYS Meshing application in ANSYS Workbench. The angle of attack is parameterised in the ANSYS geometry setup and with the desired mesh characteristics defined the mesh can be resynthesized for each angle of attack. That is, the aerofoil is rotated, the mesh redrawn and a now a more conventionally shaped domain remains aligned with the air stream. Figure 3 shows this more regularly shaped test domain, which being narrower about the wake of the aerofoil is computationally more efficient in the fluid flow calculation phase than the parabolic mesh. Figure 4 shows the irregular tri-mesh about the aerofoil, which in this illustration has a negative angle of attack. Closer to the aerofoil's surface the mesh is however a structured quad mesh which is an efficient method of packing many smaller cells close to the surface and is easily automated. This is described in more detail the following section.

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Figure 3 The 2-D unstructured mesh around an NACA 23012 aerofoil.

Figure 4 The 2-D unstructured mesh around an NACA 23012 aerofoil. Close-up of the same mesh as shown in Figure 3 in the region of the aerofoil's leading edge. Note the Inflation layer along the edge of

the aerofoil.

2.3 Mesh Refinement

A number of considerations are required when defining the refinement of the mesh, i.e. the grid spacing. Accurately capturing the boundary layer flow transitions is very important in predicting the overall aerodynamics of the test object. The friction drag very much depends on the relative amount of first laminar and then turbulent boundary layer flow along the aerofoil surface. Thus the area or volume near the surface warrants a concentration of computational resources when predicting the flow. This is manifested in the number of inflation layers about the significant aerodynamic test subjects. What is meant by inflation layers is the structured mesh cell layers that are formed from the surface of the test object; in this case the aerofoil. These can be seen as the four-sided cells (in the two-dimensional case) around the aerofoil leading edge in Figure 4 The 2-D unstructured mesh around an NACA 23012 aerofoil. Close-up of the same mesh as shown in Figure 3 in the region of the aerofoil's leading edge. Note the Inflation layer along the edge of the aerofoil. A guide to how fine the inflation layers should be and to how many layers they should extend is given by the dimensionless wall distance parameter y+ and the law of the wall[1.10][1.11][1.12]. Observance of the y+ parameter becomes pertinent in the region of transition from laminar to

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turbulent flow, in order to effectively capture the position of this transition as accurately as possible. By monitoring the size of the first layer of mesh cells, the y+ parameter can be kept within the bounds necessary to accurately model the wall friction:

3 < y+< 30 Any region where a parameter of the flow has a heightened rate of change with regard to space and/or with regard to time is worthy of extra consideration. The structured mesh shown in Figure 2 shows how density of the cells is concentrated in the wake behind the trailing edge in anticipation of a large distribution of velocities across the width of the wake.

2.4 Mesh Growth Rate

With respect to cell growth rates CFD calculations are not as robust as those of structural dynamics. Ideally the rate of growth of the cell sizes of neighbouring cells should not exceed 1.08 - 1.12. However, a rate as high as 1.25 can be tolerated and is often been employed, especially in industry in order to limit the total number of elements in the final mesh[1.14].

2.5 Boundary Conditions

The definition of the boundary conditions for such an analysis is relatively simple. As mentioned above a parabolic inlet was defined in order to be able to define the incoming air velocity, in vector form, as coming from a range of angles off the horizontal. In this way the large parabola did not have any side walls to be defined but only the inlet and outlet. Where side-walls were used they were defined as mirror surfaces as this would remove any complications of an actual wall with the drag and turbulence this would create. The test object, the aerofoil and the half-wing were defined simply as a wall, with the material set as aluminium, being a common material for aircraft wings. The initial state of the flow upstream of the aircraft is highly variable and rather difficult to assess thus the default values were simply used when defining the initial settings at the inlet for the turbulence model. For example for the SST k-ω model the specific kinetic energy was set to 1 m2s-2 and the specific dissipation rate to 1 s-1.

2.6 Solution Settings

2.6.1 Coupling

The first choice to be made was between the pressure- or density-based solver. Either of these methods work very well for the analysis of incompressible external aerodynamic flows. The pressure velocity coupling used throughout was the Coupled scheme. This scheme works for most flows other than transient ones with short time steps.

2.6.2 Spatial discretization

Suitable for tetrahedral meshes is the gradient setting of Green-Gauss Node Based. Although a computational price is paid for using this method over the cell based schemes it is more accurate when the mesh is of an irregular type, particularly when there are many skewed cells.

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The computing power in the solution phase was not a limiting factor as it had been in the creation of and handling of the mesh itself. By default when using the pressure based solver the first order upwind discretization is used. On gaining access to more powerful computing however second order discretisation was selected to improve accuracy.

2.6.3 Solution Controls

The solutions controls available allow one to adjust various relaxation factors. The default settings provided in Fluent work generally very well. On occasion when convergence of the solution was illusive at high angles of attack it was very helpful to lower these.

2.7 Viscous Models

With the unstructured mesh set up as described above the three turbulence models in the Fluent simulation; the Spalart-Allmaras, the k-ω with SST and k-kl-ω models, were compared with wind tunnel data in order to see which one is the most suitable for aerofoil simulations. An aerofoil well documented with wind tunnel data and with similar characteristics to that used on the Osqavia aircraft was the subject of this study.

2.7.1 Spalart-Allmaras Model

The Spalart-Allmaras model[1.4] was developed for wall-bounded-aerodynamic flows, and is known to work well with boundary layers subject to adverse pressure gradients but not to cope well with free shear flows.

2.7.2 The k-ω with SST Model

The SST k-ω model [1.5][1.6] is a two-equation model that has become one of the standard models used in industry. The shear stress transport (SST) formulation makes use of different context dependent approaches. Close to the wall in the boundary layer it will use the k-ω formulation. In the free stream it will switch to the k-ε formulation. Two equation models rely on the Boussinesq eddy viscosity assumption: the Reynolds stress tensor is proportional to the strain rate tensor. This works for simple flows such as in straight boundary layers. This model can predict a too greater turbulence when normal strain is large, such as when the flow is subjected to stagnation or strong acceleration. These are characteristics which are not judged to be present in such external aerodynamics applications as studied here. One option available in Fluent when using this model is the use of the Low Reynolds number

correction. By this it is referring to local Reynolds numbers of less than 1000 in the boundary layer. In the context of this study the number of cells within the boundary layer is comparatively very small in relation to the number of cells in the large scale flow around the wing.

2.7.3 The k-kl-ω Model

A three-equation eddy viscosity model[1.7], which predicts boundary layer development, i.e. transition. In order to this with any reliability it requires high cell resolution even in the stream direction. This mode in Fluent emphasises the specification of the turbulence at the inlet and turbulent decay before the leading edge of the test object is reached. In this study it

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is assumed that the incident flow is turbulent free, which can have consequences for such a model which is so dependent on the incident turbulence.

2.8 Results

Figure 5 An α-sweep of an NACA 23012 comparing the CL results of from wind tunnel tests and CFD simulations using the k-ω with SST and k-kl-ω viscous models.

Figure 5 and Figure 6 show that within a large range of angles of attack, where the flow is attached, the three turbulence models conform well to the experimental data in terms of lift, although they overestimate the drag by a significant amount. The SST k-ω model does tend to underestimate the angle at which separation of flow occurs; in the case of the NACA 23012 aerofoil roughly by about 0.1 of CL. Whilst using this model it was also observed that there could be difficulty in achieving convergence of the solution at angles of attack just below that of the angle of stall; i.e. from an angle of attack of 10° and upwards. This necessitated lowering the relaxation factors from their default values. If an absolutely stable result was not achievable the extent of the fluctuation of the flow indicated could at least be reduced in amplitude to an order of ∆CL of 0.01. The Spalart Allmaras model like the SST k-ω model performs well and gives a good prediction of the stall angle and maximum lift; on the NACA 23012 profile to within 0.1 on the CL scale. In contrast to the SST k-ω however, it can tend to overestimate the maximum lift attainable after the onset on stall has occurred, see Figure 5 An α-sweep of an NACA 23012 comparing the CL results of from wind tunnel tests and CFD simulations using the k-ω

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angle of attack /°

Wind

tunnel

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Spalart-

Allmaras

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with SST and k-kl-ω viscous models. again where the CL is overestimated at 17° to 19° degree of angle of attack. The same comparison was also made with the models applied to the current wing profile. The results, as seen in Figure 7, show again that the SST k-ω and the Spalart-Allmaras models gives a good indication of the stall angle of attack and the k-kl-ω predicts the flow to remain attached beyond the actual stall angle of attack. For both the profiles both models predict drag accurately within the range of the angles of attack where the flow is attached. There is little documentation on the k-kl-ω model. Some discussion by users in the forums indicate that they, similarly, have found it unreliable in predicting the point of flow separates from the surface, which entails that when applied to aerofoils the prediction of the stall angle is also unreliable. Although the SST k-ω model underestimates the maximum lift angle of attack this is still the preferable model for using in aircraft design; providing, as it does, a conservative prediction. Although the k-kl-ω turbulence model was also looked into for the three-dimensional simulation, for the same reasons as demonstrated here the SST k-ω model is the most suitable for this also.

Figure 6 The drag polar of the NACA 23012 aerofoil from wind tunnel tests and CFD simulations using the k-ω with SST, k-kl-ω and Spalart-Allmaras viscous models.

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Figure 7 An α-sweep of an Osquavia profile comparing the CL results of from wind tunnel tests and

CFD simulations using the SST k-ω with, k-kl-ω and Spalart-Allmaras viscous models.

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3 Study 1: The Aerofoil

3.1 Modifying the Stall Characteristics

Modifying an aerofoil by decreasing the thickness to chord ratio to produce a more slender profile will increase the stall angle. Thus following from the previous section the turbulence model selected for the rest of the project is the SST k-ω.

Figure 8 A comparison of the coefficient of lift for the Osquavia aerofoil and two of its variants

Figure 8 shows how this model is now applied to the Osquavia profile and two of its variants. Whereas the original profile has a relative thickness at the quarter chord point of 16.8%, Osquavia 130 has been reduced by a factor of 0.77 in the y-direction to give it a relative thickness of 13.0%. ECO1 is also basically the same profile but stretched by factor of 1.2 to create a more slender profile with a lower wing loading. As predicted by the theory the more slender profiles do maintain attached flow to a higher angle of attack than the original profile’s stall angle: 15° compared to ca. 13.5°. The original thick aerofoil does stall, however, in a slightly more gentle fashion. At beyond the stall angle, at an angle of attack of 23°, the coefficient of lift of the stalling original wing profile is greater than the coefficient of its variants.

3.2 Conclusion

The ECO1 aerofoil demonstrates a slightly greater maximum CL due to the thinner profile of the aerofoil but stalls more abruptly than the original wing profile with the shorter chord.

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Angle of attack /°

Osquavia 168

Osquavia 130

ECO1

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4 Study 2: Winglets

4.1 Background & Theory

Winglets, although having been known of for a long time, but have only become widespread in the relative recent era of aeronautical history. They produce a similar effect as increasing the wingspan, that is they reduce the induced drag[1.8] by diffusing the wingtip vortex. The large central inward component of the vortex is decreased whilst the small component above the tip of the winglet is slightly increased. The aerodynamic forces on the actual winglet can actually take the form of negative drag. They achieve the reduction in the aircraft’s drag at a cost in terms of structural mass and wing root bending moment, which, however, is less than that of a wingtip extension of equal aerodynamic effect. The gains of reduced induced drag are mostly obtained in high lift flight conditions, such as during take-off, climb and high altitude cruise[1.9]. Whilst the high altitude bonus may mostly be useful to large jet transports, the improvements can also be applied gainfully to general aviation where climb and turn performance can be improved. This decrease in the drag to be overcome is especially advantageous given that the propulsion power of general aviation aircraft is usually quite limited. The optimum winglet design will thus provide a reduced drag during the climb without causing detriment to the cruising efficiency due to the increased frontal area and surface area. Note that the cruise in general aviation is not generally a high CL flight condition as it is in high altitude aircraft. The winglet on the ECO1 is placed slightly rearwards with respect to the main wing in order to avoid the zone of increased flow velocity above the profile coinciding with its equivalent region of the main wing. Also, to ameliorate interference with the main wing, the winglet has a dihedral angle (not specified in this report) of less than 90° (with respect to the horizontal plane). The study will measure the aerodynamic characteristics for a small sample of different angles of toe-out of the base of the winglet.

4.2 Three-Dimensional Mesh Methods

4.2.1 Mesh Structure

Whilst setting up a structured mesh around a wing without winglets would be reasonably straight forward, setting up such a mesh about a wing with a winglet, which juts out at an angle along another axis is more complicated. Thus only unstructured meshes were created.

4.2.2 Domain Size

The rule thumb of a domain length of about 25 times the stream-wise length of the test object was difficult to abide by when working with a three-dimensional mesh. The sheer number of nodes would require too much memory of the computer and cause a failure when opening the mesh in Fluent. In order to obtain comparable results the domain, which was approximately halved in length, would be keep the same dimensions for all the different tests.

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4.3 Results

4.3.1 Comparison of a half-wing with and without a winglet

Figure 9 The variation of the lift coefficient of the half-wing with angle of attack for the wing without winglets, one with a winglet of toe-out of 2.5 ° and one with toe-out of 4.5 °

Figure 10 The variation of the drag coefficient of the half-wing with angle of attack for the wing without

winglets, one with a winglet of toe-out of 2.5 ° and one with winglet of toe-out of 4.5 °.

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From Figure 9 it can be seen that the winglets provide an increase in the coefficient of lift the from about an angle attack of 4° and up, the one with the lesser toe-out angle providing the greatest lift. Below α = 4 ° there is no significant difference in the lift provided by the different wings. Crucially in the wing without a winglet the lift curve slope, CL_α, loses its linearity for angles of attack greater than 8 °. This is the onset of stall which, although gentle in the wing without winglets sets in at a considerably lower α than the other two wings. The benefit of the winglets on CL is mirrored by their effect on CD shown in Figure 10, that is, the wings with winglets have lower drag coefficients for angles of attack between 7° and 12°. Below 7° the winglet wing with toe-out angle of 4.5° has by a small margin the greatest drag coefficient. The drag polar Figure 11 shows a region between the curves from about CL = 0.5 to 0.9 where there the half-wing with the winglets displays an advantage with a higher lift to drag ratio. This region approximately represents the angle of attack range from 6 ° to 12 °. Figure 12 shows a close up of Figure 11 with two points representing the lift to drag ratio at an angle of attack of 4° and 6°. Here one can see how that for α = 6° the half-wing with the winglet, ϑ = 4.5° has a slightly greater CD than the wing without the winglets but it also has the greater CL.

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Figure 11 Drag polar of the half-wing of the wing without winglets, with a winglet of toe-out of 2.5 ° and winglet of toe-out of 4.5 °.

Figure 12 A close up of Figure 11 showing points on the drag polar at the angle of attack of 4 ° and 6 °.

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4.3.2 Optimisation of toe-out angle of winglet segment with the help of the mesh-morphing tool

To investigate the effect of the winglet's toe-out angle further smaller increments in the angle ϑ were made by morphing the model and the mesh within the Fluent application. The two geometries available, created by CAD, have toe-out angles, ϑ, of 2.5° and 4.5°. Fluent has the facility which allows the mesh to be morphed, slightly shifting the coordinates of nodes in space but keeping the overall mesh structure. It is possible to do this to such an extent that one can rotate the angle of toe-out without having to redraw the geometry and then resynthesize the mesh, see Figure 13.

Figure 13 The mesh morphing tool in Fluent. The diagram shows the reference point defined around the winglet which can then be vectored in space to create a rotation of the toe-out angle.

This method was applied to the two models and ϑ varied a few degrees to either side. In the graphs that follow the results of the morphing of both the models are presented together with the results from a half-wing without winglets in order to display the effects on the coefficients of drag and lift.

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Figure 14 The variation of CD for the entire half-wing w.r.t. the toe-out angle of the winglet, shown for various angles of attack, α. Each angle of attack angle is represented by a pair of lines in the same colour, one for each toe-out angle defined in a CAD-model, 2.5° and 4.5°. The CD of the wing without the winglet

is shown by the dotted lines.

Figure 14 shows a small effect on the coefficient of drag. The general trend is that the decrease in CD is greater for at higher angles of attack and for greater angles of toe-out. At α = 0° one can see that the drag is in fact increased. At α = 6° the effect is also detrimental with certain angles of ϑ, i.e. between 1.5° and 4.5°. These points seem rather anomalous although the tendency for an increased drag at these values of ϑ can also be seen in the lines for the other angles of attack.

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CAD 2.5°, α = 0

CAD 2.5°, α = 2

CAD 2.5°, α = 4

CAD 2.5°, α = 6

CAD 2.5°, α = 8

CAD 4.5°, α = 0

CAD 4.5°, α = 2

CAD 4.5°, α = 4

CAD 4.5°, α = 6

CAD 4.5°, α = 8

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Figure 15 The variation of the percentage change in CD for the entire half-wing w.r.t. the toe-out angle of the winglet, shown for various angles of attack, α. Each angle of attack angle is represented by a pair of lines in the same colour, one for each toe-out angle defined in a CAD-model, 2.5 ° and 4.5 °. The percentage change of CD is defined as the difference in the in wing’s drag coefficient relative to that of the

wing without a winglet.

Figure 16 The variation of CD for just the winglet w.r.t. the toe-out angle of the winglet, shown for various angles of attack, α. Each angle of attack angle is represented by a pair of lines in the same colour, one for

each toe-out angle defined in a CAD-model, 2.5 ° and 4.5 °.

Figure 15 shows the percentage change of the drag coefficient compared to the wing without the winglet. This view amplifies the change in CD and here can be seen more clearly the

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CAD 2.5°, α = 2

CAD 2.5°, α = 4

CAD 2.5°, α = 6

CAD 2.5°, α = 8

CAD 4.5°, α = 0

CAD 4.5°, α = 2

CAD 4.5°, α = 4

CAD 4.5°, α = 6

CAD 4.5°, α = 8

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CAD 2.5°, α = 8

CAD 2.5°, α = 10

CAD 4.5°, α = 0

CAD 4.5°, α = 4

CAD 4.5°, α = 6

CAD 4.5°, α = 8

CAD 4.5°, α = 10

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detrimental effects present at an angle of attack of 6°. Also visible is the difference in CD measured on the two different CAD models but which via mesh morphing, have the same angle ϑ = 3.5 °. The difference amounts to approximately 0.5 % of the wings total CD. The coefficient of lift is less affected by the winglet. Figure 17 shows little variation of CL with ϑ. What does seem apparent is that there is a dip in the CL for ϑ = 1.5 ° and 4.5. This coincides with the increased drag at these angles of attack and indicates a flow which impairs performance.

Figure 17 The variation of overall coefficient of lift for the entire half-wing with the winglet toe-out angle for the angles of attack 4 °, 6°, 8 ° and 10 °. Each angle of attack angle is represented by a pair of lines in the same colour, one for each toe-out angle defined in a CAD-model, 2.5 ° and 4.5 °. The CL for the wing without a winglet is shown as a dotted line.

4.3.3 An analysis of the effect on CD

Comparing the CD of two similar wings where the difference is small in comparison to the overall value of CD, can be tricky as the combination of the deviations of both of them can have exaggerated and misleading effect on the difference. This may or may not be the case for the data points ϑ = 2.5 ° and 4.5 ° for α = 6 ° which deserve further investigation. Some light can be shed on this behaviour by observing the coefficient of drag on just the winglet alone, as shown in Figure 16. Here it can be seen that the smaller negative angles of ϑ produce an effect of having a higher drag on the winglet for α = 4 ° and 6 ° than for higher angles of attack. This would suggest that the bump in the graph for α = 6 ° may be part of the same phenomena rather than an anomaly. So whilst being cautious regarding the individual data points one may nevertheless draw some conclusions from the overall trend, which is that for higher angles of attack the amelioration

0,5

0,55

0,6

0,65

0,7

0,75

0,8

0,85

0,9

0,95

1

0 1 2 3 4 5 6

CL

winglet toe-out /°

CAD 2.5°, α = 4

CAD 2.5 °, α = 6

CAD 2.5°, α = 8

CAD 2.5°, α = 10

CAD 4.5°, α = 4

CAD 4.5°, α = 6

CAD 4.5°, α = 8

CAD 4.5°, α = 10

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of drag by the winglets becomes more pronounced. And that for a greater toe-out angle the drag is also decreased. Using a ϑ of less than 3.5° will give a decrease or no change in the coefficient of drag, CD, for angles of attack greater than 2°. Thereby performance is improved in the flight

regimes of wing lift coefficient of 0.7 and above and suffering a drag penalty of less than

0.75% at low coefficient of lift flight.

4.3.4 Visualisation of Winglet Effect on Wing-Tip Vortices

Use of CFD tools such as Fluent, of course, afford us of the possibility of viewing behaviour of the air flow across the aerodynamic surfaces as well just reporting the resulting data on the resulting forces. Figure 18 shows the so called diffusion of the wing-tip vortex for a relatively high lift flight condition at α = 8°. The same is described in Figure 18, showing the static pressure contours. What is apparent is the desirable characteristic of a reasonably even static pressure along the span of the winglet, indicating that the normal force is relatively even.

Figure 18 Streamlines coloured by x-velocity on the winglet at α = 8°

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Figure 19 Static pressure contours on the surface of the winglet at α = 8°

4.3.5 Visualisation of the Stall Development

First, as a reference, are shown colour-coded static pressure diagrams alongside oil-drop diagrams of the wing without winglets (turbulence model: SST k-ω). The Hi and Lo data results that are pictured in some of the following diagrams, for a plain wing and a wing with winglet of toe-out angle of 4.5°, are preliminary, because convergence or a stable oscillation has not been achieved. The high and low refer to the high and low CL

between which the simulation alternates. For angles of attack above 10° convergence could not always be achieved using the k-omega model. However, this stable ‘oscillation’, with respect to the iterations, of the forces on the wing could be achieved. This might be considered to be indicative of the unsteady flow (with respect to time) that can be observed on a stalling wing.

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Figure 20 Without winglets, alpha=6

Figure 21 Without winglets, alpha=8

Figure 22 Without winglets, alpha=10(lo)

Figure 22 and Figure 23 show the stable high and low states that the simulation alternates in between. Figure 22 does also show a larger area of circulating flow at the wing root indicating a larger region of separated flow - stall.

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Figure 23 Without winglets, alpha=10(hi)

Figure 24 Without winglets, alpha=12(lo)

Figure 25 Without winglets, alpha=14

Figure 24 and Figure 25 demonstrate the spread, with increasing α, of the stall from the wing root out along the trailing edge of the wing. The following diagrams describe the wing with winglets, with a toe-out angle of 4.5° (turbulence model: SST k-ω).

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Figure 26 With winglets, toe-out=4.5, alpha=6

Figure 27 With winglets, toe-out=4.5, alpha=8

Figure 28 With winglets, toe-out=4.5, α = 10(lo)

Comparing Figure 21 with Figure 27 one can see that the stall at wing root has started on the wing without the winglet at α = 8° but not on the wing with the winglet.

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Figure 29 With winglets, toe-out=4.5, alpha=10(hi)

Figure 30 With winglets toe-out=4.5°, α=12°

Figure 31 With winglets, toe-out=4.5, alpha=14

In comparing these high and low states diagrams main difference may be noticed at the wing root. The nature of the flow according to the oil-drop images seems also to be different, with the lower lift Figure 28 indicating stagnated flow at the very root, in contrast to the other diagram with more pronounced backflow.

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4.3.6 Discussion of the Visualisation of the Stall Development

In the static pressure contours, it is difficult to discern a significant difference between the high and low lift states recorded for the same angle of attack. Changes in these contours are very clear however, when comparing the diagrams of the different angles of attack. This can be observed here by comparing Figure 29 through Figure 31 where an area of intermediate pressure, between the low pressure of the leading edge and the high pressure of the trailing edge, spreads out more widely along the wing as α is increased. (N.B. Not all the static pressure diagrams have been given the same colour scales.) Comparing the wing without winglets to the wing with winglets set at a toe-out angle, ϑ, of 4.5 degrees: The most obvious difference in the development of the stall is that, at an angle of attack of 12° and 14°, the oil path diagram of the wing without a winglet displays separation arising from a broad section of the trailing edge about the mid-section of the span. At these same angles of attack the wing with winglet at 4.5° still only shows signs of separation at the wing root, with the rest of the wing still enjoying attached flow, most importantly over

the control services placed towards the tip of the wing on the trailing edge.

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5 Conclusions The two-dimensional study of wing profiles confirmed that out of the choice of the turbulence models, Spalart-Allmaras, k-kl-ω and SST k-ω, it was the SST k-ω proved to predict the safest, most conservative results for such external aerodynamics applications. The variations of the Osquavia design did show an increase in the angle of stall, albeit with a more abrupt stall. The chord wise lengthened aerofoil is predicted to have the highest stall angle by a small margin over the slimmed aerofoil. The three-dimensional analysis of the wing with and without winglets shows a higher maximum CL at a higher angle of stall achieved through the application of winglets. A small drag penalty is paid at low angles of attack but for flight conditions where CL is greater than 0.6 up to 1.0 there is a clear reduction in the drag. This translates into performance gains during the climb and the turn without paying a very large price in the cruise condition. The visualisation tools were used to provide an insight into the stall. Very importantly the wing with winglet showed a more favourable pattern of flow during the stall, that is, it develops from the root and maintains attached flow over the ailerons all the way up to an angle of attack of at least 14°.

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6 Further study Prediction of stall is always problematic in computational fluid dynamics. For the moment the SST k-ω appears to be the best model to use. Further experimentation which might prove fruitful in pinpointing the stall angle would be to run a time- dependent simulation; for the ‘oscillations’ often seen when having difficulty in achieving convergence reflect a real life time-dependent and unstable flow. Further, LES, whilst requiring a lot of processing power perhaps offers some potential in this field.

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7 References 1.1. http://easa.europa.eu/newsroom-and-events/press-releases/easa-certifies-aircraft-

types-under-new-light-sports-aircraft. 1.2. The Australian definition of a light sport aircraft is found in the Dictionary to the

Civil Aviation Safety Regulations. 1.3. http://www.faa.gov/aircraft/gen_av/light_sport/ 1.4. Spalart, P. R. and Allmaras, S. R. (1992), "A One-Equation Turbulence Model for

Aerodynamic Flows", AIAA Paper 92-0439 1.5. Menter, F. R. (1993), "Zonal Two Equation k-ω Turbulence Models for

Aerodynamic Flows", AIAA Paper 93-2906 1.6. Menter, F. R. (1994), "Two-Equation Eddy-Viscosity Turbulence Models for

Engineering Applications", AIAA Journal, vol. 32, no 8. pp. 1598-1605. 1.7. D. Keith Walters and Davor Cokljat (December 2008). "A three-equation eddy-

viscosity model for reynolds-averaged navier-stokes simulations of transitional flows". Journal of Fluids Engineering. 130.

1.8. Barnes W. McCormick – Aerodynamics Aeronautics & Flight Mechanics (flap effectiveness)

1.9. John J. Bertin & Michael L. Smith – Aerodynamics for Engineers 1.10. von Kármán, Th. (1930), "Mechanische Ähnlichkeit und Turbulenz", Nachrichten

von der Gesellschaft der Wissenschaften zu Göttingen, Fachgruppe 1 (Mathematik) 5: 58–76

1.11. http://www.cfd-online.com/Wiki/Dimensionless_wall_distance_%28y_plus%29 1.12. http://www.cfd-online.com/Wiki/Law_of_the_wall

1.13. Jacob Ancker, 1990 1.14. Consultation and advice from Ansys

8 Acknowledgements Niklas Anderberg and the team at Flight & Safety Design Professor Johan Revstedt at LTH Virdung at Ansys in Gothenburg

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Appendix - Some Further Notes on the Use of Fluent

1. Flight Conditions

The airspeed used in these studies was 43.8 ms-1 for the two-dimensional tests, to match the available wind tunnel data, and 33 ms-1 for the three-dimensional tests.

2. Cell Shape

The Ansys Fluent users' guide contains advice on the parameters of the mesh to help achieve a converging and reliable solution to the simulation. This includes trying to limit the number of cells with a very high skewness or of high aspect ratio close to significant parts of the flow field (e.g. near the surfaces of the test object)

3. Errors Brought To Light by Mesh Check and Case Check

Fluent warns when cells with a skewness of over 0.98 are present. It was noted that simulations that were carried out in disregard of this warning could be more likely to crash. It was found that whilst a few cells with excessive skew could be tolerated, if larger numbers were found to be of bad quality then it was better to return to the meshing application to tweak some settings regarding cell density and then to create a new mesh.

4. Mesh Smoothing and Swapping Tool

This tool is designed to improve the mesh with respect to a number of parameters using various algorithms. For the meshes used in this paper it was applied in an effort to improve the mesh after Fluent had warned of high skewness or high aspect ratios. All of these attempts were unfortunately unsuccessful and did not solve the problem or produced their own side-effects such as negative volumes. It is in fact easier to try to improve the mesh in the dedicated mesh program or, if the cells of issue are few in number and/or far from a significant aerodynamic surface, they can be tolerated without having too much of a detrimental effect on the results.

5. Steady State and Pseudo Transient Method

The pseudo transient method is a relatively recent development in the Fluent product and was found to significantly improve convergence rates without any discernible disadvantages.

6. The Use of Mesh Adaption Based On Simulation Results

This was applied in an attempt to aid convergence but rarely did so. Residuals were often found to become larger

7. Solution Settings

Relaxation factors and time scale factor proved very useful tools in attaining convergence when the standard settings do not suffice for this. The effect Fluent of double precision setting does not seem to provide any advantage as the results did not come any closer the experimental wind tunnel data for the scenarios tested in this study.

8. Turbulence model settings used

SST k-ω– The favoured model selected to be used in the analyses. Default turbulent settings were used. Spalart-Allmaras and k-kl-ω also used but not applied in the three-dimensional cases.